PURPOSE

PCTRTRS solves a triangular system of the form

where sub( A ) denotes A(IA:IA+N-1,JA:JA+N-1) and is a triangular
distributed matrix of order N, and B(IB:IB+N-1,JB:JB+NRHS-1) is an
N-by-NRHS distributed matrix denoted by sub( B ). A check is made
to verify that sub( A ) is nonsingular.

Notes
=====

Each global data object is described by an associated description
vector. This vector stores the information required to establish
the mapping between an object element and its corresponding process
and memory location.

Let A be a generic term for any 2D block cyclicly distributed array.
Such a global array has an associated description vector DESCA.
In the following comments, the character _ should be read as
"of the global array".

NOTATION STORED IN EXPLANATION
--------------- -------------- --------------------------------------
DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
DTYPE_A = 1.
CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
the BLACS process grid A is distribu-
ted over. The context itself is glo-
bal, but the handle (the integer
value) may vary.
M_A (global) DESCA( M_ ) The number of rows in the global
array A.
N_A (global) DESCA( N_ ) The number of columns in the global
array A.
MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
the rows of the array.
NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
the columns of the array.
RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
row of the array A is distributed.
CSRC_A (global) DESCA( CSRC_ ) The process column over which the
first column of the array A is
distributed.
LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
array. LLD_A >= MAX(1,LOCr(M_A)).

Let K be the number of rows or columns of a distributed matrix,
and assume that its process grid has dimension p x q.
LOCr( K ) denotes the number of elements of K that a process
would receive if K were distributed over the p processes of its
process column.
Similarly, LOCc( K ) denotes the number of elements of K that a
process would receive if K were distributed over the q processes of
its process row.
The values of LOCr() and LOCc() may be determined via a call to the
ScaLAPACK tool function, NUMROC:

The number of rows and columns to be operated on i.e the
order of the distributed submatrix sub( A ). N >= 0.

NRHS (global input) INTEGER

The number of right hand sides, i.e., the number of columns
of the distributed matrix sub( B ). NRHS >= 0.

A (local input) COMPLEX pointer into the local memory

to an array of dimension (LLD_A,LOCc(JA+N-1) ). This array
contains the local pieces of the distributed triangular
matrix sub( A ). If UPLO = 'U', the leading N-by-N upper
triangular part of sub( A ) contains the upper triangular
matrix, and the strictly lower triangular part of sub( A )
is not referenced. If UPLO = 'L', the leading N-by-N lower
triangular part of sub( A ) contains the lower triangular
matrix, and the strictly upper triangular part of sub( A )
is not referenced. If DIAG = 'U', the diagonal elements of
sub( A ) are also not referenced and are assumed to be 1.

IA (global input) INTEGER

The row index in the global array A indicating the first
row of sub( A ).

JA (global input) INTEGER

The column index in the global array A indicating the
first column of sub( A ).

DESCA (global and local input) INTEGER array of dimension DLEN_.

The array descriptor for the distributed matrix A.

B (local input/local output) COMPLEX pointer into the

local memory to an array of dimension
(LLD_B,LOCc(JB+NRHS-1)). On entry, this array contains the
local pieces of the right hand side distributed matrix
sub( B ). On exit, if INFO = 0, sub( B ) is overwritten by
the solution matrix X.

IB (global input) INTEGER

The row index in the global array B indicating the first
row of sub( B ).

JB (global input) INTEGER

The column index in the global array B indicating the
first column of sub( B ).

DESCB (global and local input) INTEGER array of dimension DLEN_.

The array descriptor for the distributed matrix B.

INFO (output) INTEGER

= 0: successful exit
< 0: If the i-th argument is an array and the j-entry had
an illegal value, then INFO = -(i*100+j), if the i-th
argument is a scalar and had an illegal value, then
INFO = -i.
> 0: If INFO = i, the i-th diagonal element of sub( A ) is
zero, indicating that the submatrix is singular and the
solutions X have not been computed.